where \( a_{\ell }\)  and \( b_{\ell }\)  are the Mie scattering coefficients corresponding to the transverse magnetic and
transverse electric modes, respectively. The index \(\ell \)  is used to denote \(\ell ^{th}\)  order spherical harmonic channel and \(x = kr\)  is size parameter with \(k=2\pi /\lambda \) .
The Mie scattering coefficients can be derived by employing the boundary conditions on the surface of the scatterer and written as [1]}
\(a_{\ell }= \frac{m\psi _{\ell }(mx) \psi ^{\prime }_{\ell }(x)-\mu \psi _{\ell }(x) \psi ^{\prime }_{\ell }(mx)}{m\psi _{\ell }(mx) \xi ^{\prime }_\ell (x)-\mu \xi _\ell (x) \psi ^{\prime }_{\ell }(mx)}, \) 
\(b_{\ell }= \frac{\mu \psi _{\ell }(mx) \psi ^{\prime }_{\ell }(x)-m \psi _{\ell }(x) \psi ^{\prime }_{\ell }(mx) }{\mu \psi _{\ell }(mx) \xi ^{\prime }_\ell (x)-m\xi _\ell (x)\psi ^{\prime }_{\ell }(mx) }, \) 
